I have always understood that our current 3 term school year, (beginning early January, April after Easter and early September,) fell into practise around the summer harvest time in August??
When I first went to school, in Scotland, the holidays were New Year (which usually began on Christmas Eve), Easter, summer (end of June to mid/late August) and the tattie (potato) holidays in mid October. The holidays were scheduled to allow schoolchildren to help with the soft fruit harvest in summer and the tattie harvest in autumn. All except the summer holidays were one or two weeks, and the 'Lower' and 'Higher' exams were held in May. (The corresponding exams still are - my 15-year-old neighbour just finished his exams last week.)
Later on I attended a school which was tied largely to the dates of the English 'O and 'A' level exams, which were in July. We had about three weeks' holiday over Christmas/New Year, four weeks in April, and then late July to mid-September. This meant we were cooped up in school at the best time of year, the early summer, and that the autumn term always seemed to loom very long, sometimes as long as 13 weeks without a break
I've just taken a keek at the current school dates for this area - the holidays in 2019/2020 are 14 to 25 October (2 weeks), 23 December to 3 January (2 weeks), 30 March to 10 April (two weeks) and 3 July to 17 August (six weeks plus 2 days).
According to Mr Google the English dates in 2019 are 17 to 20 February (1 week), 8 to 26 April (3 weeks), 27 to 31 May (1 week), 15 July to 6 September (8 weeks), 21 to 25 October (1 week), 23 December to 3 January (2 weeks). However at least one English school authority's dates don't quite match these, although they vary only by a few days either way.